# Sarkozy's theorem in function fields

@article{Green2016SarkozysTI,
title={Sarkozy's theorem in function fields},
author={B. Green},
journal={arXiv: Number Theory},
year={2016}
}
• B. Green
• Published 2016
• Mathematics
• arXiv: Number Theory
S\'ark\"ozy proved that dense sets of integers contain two elements differing by a $k$th power. The bounds in quantitative versions of this theorem are rather weak compared to what is expected. We prove a version of S\'ark\"ozy's theorem for polynomials over $\mathbb{F}_q$ with polynomial dependencies in the parameters. More precisely, let $P_{q,n}$ be the space of polynomials over $\mathbb{F}_q$ of degree $2q^{(1 - c(k,q))n}$, then $A$ contains distinct polynomials $p(T), p'(T)$ such that \$p… Expand
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